Reconstruction algorithms for source term recovery from dynamical samples in catalyst models
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911766245539840 |
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| author | Aldroubi, Akram Gong, Le Krishtal, Ilya Miller, Brendan Thareja, Sumati |
| author_facet | Aldroubi, Akram Gong, Le Krishtal, Ilya Miller, Brendan Thareja, Sumati |
| contents | This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the form $F=h+η$, where $η$ is a Lipschitz continuous background source. The primary objective is to estimate the unknown parameters of non-instantaneous sources $h(t)=\sum\limits_{j=0}^M h_je^{-ρ_j(t-t_j)}χ_{[t_j,\infty)}(t)$, such as the decay rates, initial intensities and activation times. We present two novel recovery algorithms that employ distinct sampling methods of the solution of the IVP. Algorithm 1 combines discrete and weighted average measurements, whereas Algorithm 2 uses a different variant of weighted average measurements. We analyze the performance of these algorithms, providing upper bounds on the recovery errors of the model parameters. Our focus is on the structure of the dynamical samples used by the algorithms and on the error guarantees they yield. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction algorithms for source term recovery from dynamical samples in catalyst models Aldroubi, Akram Gong, Le Krishtal, Ilya Miller, Brendan Thareja, Sumati Dynamical Systems Functional Analysis This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the form $F=h+η$, where $η$ is a Lipschitz continuous background source. The primary objective is to estimate the unknown parameters of non-instantaneous sources $h(t)=\sum\limits_{j=0}^M h_je^{-ρ_j(t-t_j)}χ_{[t_j,\infty)}(t)$, such as the decay rates, initial intensities and activation times. We present two novel recovery algorithms that employ distinct sampling methods of the solution of the IVP. Algorithm 1 combines discrete and weighted average measurements, whereas Algorithm 2 uses a different variant of weighted average measurements. We analyze the performance of these algorithms, providing upper bounds on the recovery errors of the model parameters. Our focus is on the structure of the dynamical samples used by the algorithms and on the error guarantees they yield. |
| title | Reconstruction algorithms for source term recovery from dynamical samples in catalyst models |
| topic | Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2401.15460 |